where \(\nu _t\)  is the unique solution to the mean-field equation (REF ) with initial datum \(\bar{\nu }\) . As mentioned in the introduction, while for interacting particle systems with the number of particles fixed at \(n\in \mathbb {N}\)  this would imply narrow convergence of the \(k\) -marginals at time \(t\)  to \(\nu _t^{\otimes k}\)  (e.g. see [1]}), in our setting this implies convergence of the \(k\) -correlation functions [2]}.
